NSW Health confirmed on Thursday the baby contracted the Omicron variant and was treated at the John Hunter Hospital in December 2021.
They had no underlying health conditions.
"NSW Health offers its heartfelt condolences to the family and asks that their privacy be respected during this most difficult time," it said in a statement.
The baby's death was referred to the NSW Coroner after it was reported in January.
The news of the baby's death comes just two days after a two-year-old died of COVID-19 in Sydney.
NSW has had 2044 COVID-19 related deaths since the start of the pandemic.